CN111783189A - Method for judging reasonable bracket height of layered pouring concrete - Google Patents

Method for judging reasonable bracket height of layered pouring concrete Download PDF

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CN111783189A
CN111783189A CN202010469183.7A CN202010469183A CN111783189A CN 111783189 A CN111783189 A CN 111783189A CN 202010469183 A CN202010469183 A CN 202010469183A CN 111783189 A CN111783189 A CN 111783189A
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concrete
concrete beam
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于孟生
肖华杰
马跃腾
姚鑫玉
成魁
黄远
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Nanning Urban Construction Investment Development Co ltd
Guangxi Jiaoke Group Co Ltd
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Guangxi Jiaoke Group Co Ltd
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Abstract

The invention relates to the field of bridge and culvert engineering in the transportation industry, and particularly discloses a method for judging the height of a reasonable bracket for pouring concrete in a layered mode. However, for the cast-in-place of the support, particularly for the full-hall support supporting and layered pouring of the concrete beam, the height and the rigidity of the support are mutually linked, so that the stress of the first-layer concrete beam is influenced. The early-stage poured concrete is easy to generate tensile stress in a pier top negative bending moment area or a midspan maximum positive bending moment area to form initial tensile strain, so that the early stress of the concrete generates larger creep in the later period, the stress reserve in the bridge forming stage is reduced, and the beam body concrete is cracked when the tensile stress reaches the tensile strength of the concrete. The invention provides a method for judging reasonable bracket height of the layered cast concrete based on the stress safety state of the first beam of the layered cast concrete beam, and during specific construction, an optimal bracket scheme is selected, so that the time and the cost are saved for actual production, and the method has good engineering and economic benefits.

Description

Method for judging reasonable bracket height of layered pouring concrete
Technical Field
The invention relates to the field of bridge and culvert engineering in the transportation industry, and provides a method for judging the height of a reasonable bracket of layered pouring concrete based on the stress safety state of a first-layer beam of the layered pouring concrete beam.
Background
Concrete bridges are widely used in bridge construction with the advantages of good stress performance, service performance, construction maturity and the like. Most concrete beams are not formed by one-time pouring, and particularly, the concrete beams with higher beam height or complicated detailed structures generally need to be poured in layers for many times. However, for the cast-in-place of the support, particularly for the full-hall support supporting and layered concrete pouring of the beam, the height and the rigidity of the support are mutually linked, so that the stress condition of the first-layer concrete beam is limited. The early-stage poured concrete is easy to generate tensile stress in a pier top negative bending moment area or a midspan maximum positive bending moment area to form initial tensile strain, so that the early stress of the concrete generates larger later-stage creep, the stress reserve in a bridge forming stage is reduced, and the beam body concrete is cracked when the tensile stress reaches the tensile strength of the concrete. And the stress condition of the subsequent cast concrete beam on the first layer is directly determined by different full houses, the first layer concrete beam generates bending moment deformation at the moment, the tensile stress appears at the bottom of the span beam, and if the height of the support is unreasonable, the first layer concrete beam is easy to crack, so that the safety and the durability of the concrete beam are influenced.
Disclosure of Invention
The invention aims to provide a method for judging the reasonable height of a layered casting concrete beam support, which adopts an elastomechanics plane problem analysis method, takes the subsequent casting concrete as load, deduces the stress function of the first layer concrete beam in a system, combines the concrete strength development law, and configures the reasonable full support height under the condition of ensuring the stress of the first layer concrete beam.
In order to achieve the purpose, the invention provides a method for judging the height of a reasonable bracket for layered casting of concrete, which specifically comprises the following steps:
s1, erecting a full-hall support on the foundation, laying a template on the full-hall support, binding a first layer of reinforcing steel bars on the template after pre-pressing the full-hall support, pouring a first layer of concrete beam, binding reinforcing steel bars of a second layer of concrete beam when the first layer of concrete beam is hardened to a certain strength, and pouring the second layer of concrete beam;
s2, acquiring the length of the equal-section concrete beam of the first-layer concrete beam and the uniform load of the second-layer concrete beam on the first-layer concrete beam;
s3, simulating the action of the full framing on the first concrete beam by adopting an analysis model with an elastic support, and constructing a differential equation of the first concrete beam by combining the uniform load of the second concrete beam on the first concrete beam;
s4, solving a differential equation to obtain the tensile stress of the first-layer concrete beam;
s5, obtaining the compressive strength of the first-layer concrete beam, and obtaining the maximum tensile strength of the first-layer concrete beam according to the compressive strength;
s6, solving according to the relation between the tensile stress and the maximum tensile strength of the first-layer concrete beam to obtain the allowable weight of the second-layer concrete beam;
and S7, under the conditions of the allowable maximum tensile strength and the allowable weight of the second-layer concrete beam, solving an implicit function unknown quantity according to the relation between the tensile stress of the first-layer concrete beam and the maximum tensile strength, and solving the allowable height of the full framing according to the implicit function unknown quantity.
Preferably, in the above technical solution, the stiffness coefficient of the analysis model with elastic support is:
Figure BDA0002513712770000021
formula (1) wherein: em is the modulus of elasticity of the scaffold material; hm is the height of the full support; am is the area of the supporting section of the full support per square meter; i ismyAnd ImzThe inertia moments of the Y axis and the Z axis of the full support are respectively; mu is Poisson's ratio. Because the full framing is mainly resistant to compression, neglecting shearing and bending torsion, the spring stiffness K of the full framing is Em/Hm per linear meter.
Preferably, in the above technical solution, according to a beam deflection differential equation and a coordination condition of the support top settlement S and the deflection deformation of the first-layer beam, S ═ ω, that is:
P＝K0S＝K0ω (2)
K0the elastic coefficient of the bracket system represents the pressure intensity required by unit deformation; p is the pressure strength of any point on the top of the bracket; s is vertical deformation at the action position of P, and omega is the deflection of the first-layer concrete beam;
according to elasto-mechanical analysis, the beam equation:
Figure BDA0002513712770000022
Figure BDA0002513712770000023
Figure BDA0002513712770000024
formula (3)) -in equation (5): m is the bending moment to which the concrete beam is subjected, FsThe shear force borne by the first-layer concrete beam, E is the elastic modulus of the first-layer concrete beam, omega is the deflection of the first-layer concrete beam, and P (x) is the uniform load on the micro-section of the first-layer concrete beam
Preferably, in the above technical solution, in step S3, in step S4, the equation (3) is applied, and the basic differential equation of the primary beam of the elastic support under the foundation is considered as:
Figure BDA0002513712770000031
Figure BDA0002513712770000032
in step S4:
Figure BDA0002513712770000033
EI is the section bending rigidity;
the solution of equation (7) is:
Figure BDA0002513712770000034
the boundary condition is
Figure BDA0002513712770000035
Then: c3′＝C4′＝0
Order to
Figure BDA0002513712770000036
Δ' ═ cosh2 γ + cos2 γ then:
Figure BDA0002513712770000037
therefore, the temperature of the molten metal is controlled,
Figure BDA0002513712770000038
substituting the formula (8) to obtain:
Figure BDA0002513712770000039
solving to obtain:
Figure BDA00025137127700000310
preferably, in the above technical solution, in step S3, the basic differential equation of the elastic support first beam without considering the foundation is as follows:
Figure BDA00025137127700000311
in step S4, the following are set:
Figure BDA00025137127700000312
EI is the section bending rigidity;
the solution of equation (8) is:
Figure BDA00025137127700000313
the boundary condition is
Figure BDA00025137127700000314
Then: c3＝C4＝0
Order to
Figure BDA0002513712770000041
Δ cosh2 α + cos2 α then:
similarly, the stress function of the elastic support first-layer beam under the foundation is not considered in the solution
Figure BDA0002513712770000042
Preferably, in the above technical solution, in step S5, the tensile strength f of the first-layer concrete beamt,nTo compressive strength fcu,n0.05 times, i.e. ft,n＝0.05fcu,n；
In step S6, the first concrete layer is not formedNow crack, must satisfy sigma<ft,nI.e. by
Considering the foundation as follows:
Figure BDA0002513712770000043
simplified backstage type (15)
Figure BDA0002513712770000044
The allowable weight of the second layer of concrete is as follows:
Figure BDA0002513712770000045
in step S7, f is allowedt,n、p0Then, the unknown quantity β of implicit function is solved by the formula (15)
Figure BDA0002513712770000046
The height allowed for the stent system is then:
Figure BDA0002513712770000047
formula (17) wherein: h (m) is the allowable height of the support system.
Preferably, in the above technical solution, in step S5, the tensile strength f of the first-layer concrete beamt,nTo compressive strength fcu,n0.05 times, i.e. ft,n＝0.05fcu,n；
In step S6, the first concrete layer does not crack and must satisfy the requirement of sigma<ft,nI.e. by
Regardless of the foundation:
Figure BDA0002513712770000048
simplified backstage formula (19)
Figure BDA0002513712770000049
The allowable weight of the second layer of concrete is as follows:
Figure BDA00025137127700000410
in step S7, f is allowedt,n、p0In this way, the implicit function unknowns are solved from equation (18)
Figure BDA0002513712770000051
Then
Figure BDA0002513712770000052
Figure BDA0002513712770000053
The height allowed for the stent system is then:
Figure BDA0002513712770000054
formula (21) wherein: h (m) is the allowable height of the support system.
Compared with the prior art, the invention has the beneficial effects that:
the reasonable height configuration method for the layered casting concrete support is based on an elastic mechanics theory, deduces the stress of the first layer concrete beam when the second layer concrete is cast, and determines the reasonable support height of the first layer concrete beam under the stress safety according to the compression strength test value of the same batch of concrete cube test blocks of the first layer concrete beam. This patent can effectively instruct to adopt the layering to pour the reasonable height of support, can guarantee the safety of beam bottom stress, can guarantee the cost again, has good economic benefits.
Drawings
FIG. 1 is a simplified model of the equivalent elastic simply supported beam uniformly loaded without considering the foundation.
FIG. 2 is a simplified model of the invention for the equivalent elastic simply supported beam to be uniformly loaded under the condition of considering the foundation.
FIG. 3 is a schematic view of a stent according to the present invention.
FIG. 4 is a diagram of a finite element model.
FIG. 5 is a first comparison of the analytical solution and finite element calculation results of the present invention.
FIG. 6 is a second comparison of the analytic solution and finite element calculation results of the present invention.
Detailed Description
Specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings, but it should be understood that the scope of the present invention is not limited to the specific embodiments.
In this embodiment, the method for judging the reasonable bracket height in the layered casting of concrete specifically includes:
firstly, the stress mechanism and the state of a first-layer concrete beam are analyzed in the construction process of adopting a support to pour the concrete beam in a layering way. And binding reinforcing steel bars on the template according to a design drawing, pouring the first layer of concrete, binding the reinforcing steel bars of the second layer of concrete beam when the concrete is hardened and reaches a certain strength, and pouring the second layer of concrete. The construction process is analyzed, and the foundation under the first concrete beam provides upward supporting force for balancing the dead weight of the first-layer concrete beam and the steel bars and the concrete gravity of the second-layer beam. The inventor finds out through a large number of engineering actual measurements that when reinforcing steel bars of two-layer beams are bound and concrete is poured, the foundation base is unevenly compressed under the action of the reinforcing steel bars and the concrete of the two-layer beams, so that the first-layer concrete beam is deformed, the midspan deformation is large, the deformation gradually changes to zero at a support, the tensile stress appears near the midspan of the bottom of the first-layer concrete beam, the early initial strain and the later creep increase are generated, and when the tensile stress is greater than the concrete strength at that time, the first-layer concrete beam cracks, and safety and resistance accidents occur.
In summary, in order to ensure that the first-layer concrete beam does not crack, the stress value of the first-layer concrete beam needs to be obtained, and the stress value solving process is as follows:
based on the analysis, the reinforcement binding and concrete pouring construction of the two-layer beam are regarded as loads acting on the first-layer concrete beam and the support, and the following assumptions are made:
(1) simplified analysis is carried out on the first layer of formed concrete beam which is cast by the full-framing in a layered mode, wherein the length of the concrete beam with the equal section is L, the beam end is simply supported, concrete is cast by the full-framing in a layered mode, and uniformly distributed loads P are used0The effect of the steel reinforcement and concrete of the second layer beam on the first layer was simulated, and due to the symmetry of the problem, the origin of coordinates was taken at the midpoint of the beam, as shown in fig. 1 and 2.
(2) The existence of the support of the full support of the actual beam structure can simulate the effect of the support on the concrete beam by adopting an analysis model with an elastic support. The conversion matrix method is adopted, and the middle part is provided with an elastic support. The full-space support is processed according to an elastic foundation, the rigidity coefficient of the full-space support is K, the counter force of the elastic foundation is in direct proportion to the deflection omega of the first-layer beam, the direction of the counter force is opposite to omega, for the full-space support, the elastic support is used for simulating the action on the first-layer beam, the elastic constraint coupling effect is calculated and considered, at the moment, the general elastic support type is shown in the following formula (1), non-zero values except the diagonal line in the formula are the effect of considering the mutual influence and the mutual correlation of certain degrees of freedom, and the horizontal elastic support is not considered.
Formula (1) wherein: em is the modulus of elasticity of the scaffold material; hm is the height of the full support; am is the area of the supporting section of the full support per square meter; i ismyAnd ImzThe inertia moments of the Y axis and the Z axis of the full support are respectively; mu is Poisson's ratio. Because the full framing is mainly resistant to compression, neglecting shearing and bending torsion, the spring stiffness K of the full framing is Em/Hm per linear meter.
Figure BDA0002513712770000061
(3) The pressure intensity of any point on the top of the bracket is in direct proportion to the vertical deformation S of the point, and P is equal to K0S，K0The foundation bed coefficient represents the pressure intensity required for generating unit deformation; p is the pressure strength of any point on the top of the bracket; s is the vertical deformation at the p-action position. According to the flexural differential equation of the beam and the coordination condition of the support top settlement S and the flexural deformation of the first-layer beam, S is omega, namely:
P＝K0S＝K0ω (2)
according to the related knowledge of elastic mechanics, the equation of the beam is as follows:
Figure BDA0002513712770000071
Figure BDA0002513712770000072
Figure BDA0002513712770000073
in formulae (3) to (5): m is the bending moment to which the concrete beam is subjected, FsThe shearing force borne by the first-layer concrete beam, E is the elastic modulus of the first-layer concrete beam, omega is the deflection of the first-layer concrete beam, and P (x) is the uniform load on the micro-section of the first-layer concrete beam. Applying equation (3), the basic differential equation of the elastic support first-layer beam under the foundation is considered as follows:
Figure BDA0002513712770000074
Figure BDA0002513712770000075
suppose that:
Figure BDA0002513712770000076
the solution of equation (7) is:
Figure BDA0002513712770000077
the boundary condition is
Figure BDA0002513712770000078
Then: c3′＝C4′＝0
Order to
Figure BDA0002513712770000079
Δ' ═ cosh2 γ + cos2 γ then:
Figure BDA00025137127700000710
therefore, the temperature of the molten metal is controlled,
Figure BDA00025137127700000711
substituting formula (9) to obtain:
Figure BDA00025137127700000712
solving to obtain:
Figure BDA00025137127700000713
the basic differential equation for the spring-loaded first-layer beam without considering the foundation is:
Figure BDA0002513712770000081
suppose that:
Figure BDA0002513712770000082
the solution of equation (8) is:
Figure BDA0002513712770000083
the boundary condition is
Figure BDA0002513712770000084
Then: c3＝C4＝0
Order to
Figure BDA0002513712770000085
Δ cosh2 α + cos2 α then:
similarly, the stress function of the elastic support first-layer beam under the foundation is not considered in the solution
Figure BDA0002513712770000086
When the second layer of beam steel bars are bound and concrete is poured, the age of the first layer of concrete is n days, and when the first layer of concrete is cured for n days under the same condition with the same batch of concrete cubic test blocks of the first layer of concrete, the average value of the test compressive strength of the first layer of concrete is fcu,nBased on the relationship between the compressive strength and the tensile strength of the concrete, namely, the tensile strength of the concrete is generally 0.05-0.1 times of the compressive strength, considering the non-uniformity and the size effect of the concrete, the invention safely takes the tensile strength of the concrete as 0.05 times of the compressive strength, namely ft,n＝ 0.05fcu,n。
The first layer concrete does not crack, so that the safety and the tolerance of the first layer concrete beam can be ensured, and the requirement of sigma must be met<ft,nI.e. by
(1) Considering the foundation as follows:
Figure BDA0002513712770000087
simplified backstage formula (12)
Figure BDA0002513712770000088
At the allowable ft,n、p0Then, the implicit function unknown quantity β is solved by the formula (14)
Figure BDA0002513712770000089
The height allowed for the scaffolding system is then:
Figure BDA00025137127700000810
(2) regardless of the foundation:
Figure BDA00025137127700000811
simplified backstage type (18)
Figure BDA0002513712770000091
At the allowable ft,n、p0Next, the implicit function unknowns are solved by equation (17)
Figure BDA0002513712770000092
Then
Figure BDA0002513712770000093
The height allowed for the stent system is then:
Figure BDA0002513712770000094
example 1
For a simple beam bridge, the minimum clearance height under the bridge is 6.0 m, the automobile load grade is highway-I grade, and a support is arranged on a strip foundation
Figure BDA0002513712770000096
Spiral steel pipes are shown in fig. 4 below. The height is poured to the first section 500mm, and when the first floor roof beam belongs to the simply supported beam atress, the height should be taken up in total height 0.3 ~ 0.7 to the first floor height of pouring, and the height is poured to the second section, and the priority considers the construction joint and sets up near neutral axis, divides behind the construction joint, pours the layer equivalence with two layers and is the support system of equipartition load transmission to the first floor. Wherein the full-hall support is simulated by adopting elastic supports with rigidity, one elastic support is distributed every 60cm, 50 elastic supports are distributed in 30m span, and the rigidity of the elastic support is 106According to the actual working conditions of the model, the concrete material is defined as C50 concrete, the height × width of the section size of the first layer of concrete is 0.5m × 1m, the second layer of concrete is loaded on the first layer of concrete in a uniformly distributed load mode, the uniformly distributed load q is 0.5 × 1.0 × 25 is 12.5kN/m, a simple supporting beam in the model should restrict three translational degrees of freedom and two rotational degrees of freedom at the left end of the beam, the negative Z axis is taken as the gravity direction, the X axis is taken as the axial length, and the concrete material is C50 concreteAnd the right end of the beam restrains the translational freedom degrees of Y and Z directions and the rotational freedom degrees of X and Z directions.
The numerical calculation method of the finite element is adopted for verification, as shown in the following table 1 and fig. 3, the calculation is better consistent with the finite element result curve, and the analytic solution is accurate and correct, as shown in fig. 5 and fig. 6.
TABLE 1 comparative analysis of stress results (unit: MPa)
Table 1 Comparative analysis ofstress results(Unit:MPa)
Figure BDA0002513712770000095
The embodiment discloses a method for judging the reasonable support height of layered casting concrete, wherein a full-hall support is erected on a foundation, a template is laid on the full-hall support, a first layer of reinforcing steel bars are bound on the template after the full-hall support is pre-pressed, a beam end is a simple support, a first layer of concrete beam is cast, when the first layer of concrete beam is hardened to a certain strength, reinforcing steel bars of a second layer of concrete beam are bound, and the second layer of concrete beam is cast; the method for judging the reasonable support height of the layered casting concrete specifically comprises the following steps:
the parameter acquisition module is used for acquiring the length of the equal-section concrete beam of the first layer of concrete beam and the uniform load of the second layer of concrete beam on the first layer of concrete beam;
the differential equation establishing module is used for simulating the action of the full framing on the first-layer concrete beam by adopting an analysis model with an elastic support and establishing a differential equation of the first-layer concrete beam by combining uniform load of the second-layer concrete beam on the first-layer concrete beam;
the differential equation solving module is used for solving a differential equation to obtain the tensile stress of the first-layer concrete beam;
the maximum tensile strength acquisition module is used for acquiring the compressive strength of the first-layer concrete beam and acquiring the maximum tensile strength of the first-layer concrete beam according to the compressive strength;
the allowable weight obtaining module is used for solving according to the relation between the tensile stress and the maximum tensile strength of the first-layer concrete beam to obtain the allowable weight of the second-layer concrete beam;
and the allowable height acquisition module is used for solving an implicit function unknown quantity according to the relation between the tensile stress and the maximum tensile strength of the first layer concrete beam under the allowable maximum tensile strength and the allowable weight of the second layer concrete beam, and solving the allowable height of the full support according to the implicit function unknown quantity.
Further, the rigidity coefficient of the analysis model with the elastic support is as follows:
Figure BDA0002513712770000101
formula (20) wherein: em is the modulus of elasticity of the scaffold material; hm is the height of the full support; am is the area of the supporting section of the full support per square meter; i ismyAnd ImzThe inertia moments of the Y axis and the Z axis of the full support are respectively; mu is Poisson's ratio. Because the full framing is mainly resistant to compression, neglecting shearing and bending torsion, the spring stiffness K of the full framing is Em/Hm per linear meter.
Further, according to the flexural differential equation of the beam and the coordination condition of the support top settlement S and the flexural deformation of the first-layer beam, S is ω, that is:
P＝K0S＝K0ω (21)
K0the elastic coefficient of the bracket system represents the pressure intensity required by unit deformation; p is the pressure strength of any point on the top of the bracket; s is vertical deformation at the action position of P, and omega is the deflection of the first-layer concrete beam;
according to elasto-mechanical analysis, the beam equation:
Figure BDA0002513712770000111
Figure BDA0002513712770000112
Figure BDA0002513712770000113
in formulae (22) to (24): m is the bending moment to which the concrete beam is subjected, FsThe shear force borne by the first-layer concrete beam, E is the elastic modulus of the first-layer concrete beam, omega is the deflection of the first-layer concrete beam, and P (x) is the uniform load on the micro-section of the first-layer concrete beam
Further, in step S3, in step S4, equation (22) is applied, and the basic differential equation of the primary beam of the elastic support under the foundation is considered as follows:
Figure BDA0002513712770000114
Figure BDA0002513712770000115
in step S4:
Figure BDA0002513712770000116
EI is the section bending rigidity;
the solution of equation (26) is:
Figure BDA0002513712770000117
the boundary condition is
Figure BDA0002513712770000118
Then: c3′＝C4′＝0
Order to
Figure BDA0002513712770000119
Δ' ═ cosh2 γ + cos2 γ then:
Figure BDA00025137127700001110
therefore, the temperature of the molten metal is controlled,
Figure BDA00025137127700001111
substituting the formula (8) to obtain:
Figure BDA00025137127700001112
solving to obtain:
Figure BDA00025137127700001113
further, applying equation (22), the basic differential equation of the elastic support first-layer beam without considering the foundation is:
Figure BDA0002513712770000121
setting:
Figure BDA0002513712770000122
EI is the section bending rigidity;
the solution of equation (27) is:
Figure BDA0002513712770000123
the boundary condition is
Figure BDA0002513712770000124
Then: c3＝C4＝0
Order to
Figure BDA0002513712770000125
Δ cosh2 α + cos2 α then:
similarly, the stress function of the elastic support first-layer beam under the foundation is not considered in the solution
Figure BDA0002513712770000126
Further, the tensile strength f of the first-layer concrete beamt,nTo compressive strength fcu,n0.05 times, i.e. ft,n＝0.05fcu,n；
The first layer concrete does not crack and must meet the requirement of sigma<ft,nI.e. by
Considering the foundation as follows:
Figure BDA0002513712770000127
simplified backstage type (34)
Figure BDA0002513712770000128
The allowable weight of the second layer of concrete is as follows:
Figure BDA0002513712770000129
at the allowable ft,n、p0Then, the implicit function unknown β is solved from the formula (34), and
Figure BDA00025137127700001210
the height allowed for the scaffolding system is then:
Figure BDA00025137127700001211
formula (36) wherein: h (m) is the allowable height of the support system.
Further, the tensile strength f of the first-layer concrete beamt,nTo compressive strength fcu,n0.05 times, i.e. ft,n＝0.05fcu,n；
The first layer concrete does not crack and must meet the requirement of sigma<ft,nI.e. by
Regardless of the foundation:
Figure BDA00025137127700001212
simplified backstage type (38)
Figure BDA0002513712770000131
The allowable weight of the second layer of concrete is as follows:
Figure BDA0002513712770000132
at the allowable ft,n、p0In the following, the implicit function unknowns are solved by equation (39)
Figure BDA0002513712770000133
Then
Figure BDA0002513712770000134
The height allowed for the stent system is then:
Figure BDA0002513712770000135
formula (40) wherein: h (m) is the allowable height of the support system.
In conclusion, the method is based on the elastomechanics plane problem analysis, the subsequent pouring concrete is used as the load, the foundation, the support, the primary concrete beam and the subsequent pouring concrete are really a force transmission system, and the method for judging the reasonable support height of the layered pouring concrete is provided. The method is based on an elastic mechanics plane problem analysis method, a stress function of a first-layer concrete beam is deduced, a judgment method for reasonable support height of the layered poured concrete is provided, during specific construction, an optimal support scheme is selected, and feasibility of the judgment method is demonstrated through mutual verification with finite element calculation, so that time and cost are saved for actual production, and good engineering and economic benefits are achieved.

Claims (7)

1. The method for judging the reasonable support height of the layered pouring concrete is characterized by specifically comprising the following steps of:
s1, erecting a full-hall support on the foundation, laying a template on the full-hall support, binding a first layer of reinforcing steel bars on the template after pre-pressing the full-hall support, pouring a first layer of concrete beam when the beam end is a simple support, binding reinforcing steel bars of a second layer of concrete beam when the first layer of concrete beam is hardened to a certain strength, and pouring the second layer of concrete beam;
s2, acquiring the length of the equal-section concrete beam of the first-layer concrete beam and the uniform load of the second-layer concrete beam on the first-layer concrete beam;
s3, simulating the action of the full framing on the first concrete beam by adopting an analysis model with an elastic support, and constructing a differential equation of the first concrete beam by combining the uniform load of the second concrete beam on the first concrete beam;
s4, solving a differential equation to obtain the tensile stress of the first-layer concrete beam;
s5, obtaining the compressive strength of the first-layer concrete beam, and obtaining the maximum tensile strength of the first-layer concrete beam according to the compressive strength;
s6, solving according to the relation between the tensile stress and the maximum tensile strength of the first-layer concrete beam to obtain the allowable weight of the second-layer concrete beam;
and S7, under the conditions of the allowable maximum tensile strength and the allowable weight of the second-layer concrete beam, solving an implicit function unknown quantity according to the relation between the tensile stress of the first-layer concrete beam and the maximum tensile strength, and solving the allowable height of the full framing according to the implicit function unknown quantity.
2. The method for judging the reasonable height of the layered casting concrete according to claim 1, wherein the rigidity coefficient of the analysis model with the elastic support is as follows:
Figure FDA0002513712760000011
formula (1) wherein: em is the modulus of elasticity of the scaffold material; hm is the height of the full support; am is the area of the supporting section of the full support per square meter; i ismyAnd ImzThe inertia moments of the Y axis and the Z axis of the full support are respectively; mu is Poisson's ratio. Because the full framing is mainly resistant to compression, neglecting shearing and bending torsion, the spring stiffness K of the full framing is Em/Hm per linear meter.
3. The method for judging the reasonable height of the cast-in-place concrete according to claim 2, wherein according to the flexural differential equation of the beam and the coordination condition of the support top settlement S and the flexural deformation of the first-layer beam, S ═ ω, namely:
P＝K0S＝K0ω (2)
K0the elastic coefficient of the bracket system represents the pressure intensity required by unit deformation; p is the pressure strength of any point on the top of the bracket; s is vertical deformation at the action position of P, and omega is the deflection of the first-layer concrete beam;
according to elasto-mechanical analysis, the beam equation:
Figure FDA0002513712760000021
Figure FDA0002513712760000022
Figure FDA0002513712760000023
in formulae (3) to (5): m is the bending moment of the concrete beam, Fs is the shearing force of the first layer of concrete beam, E is the elastic modulus of the first layer of concrete beam, omega is the deflection of the first layer of concrete beam, and P (x) is the uniform load on the micro-section of the first layer of concrete beam.
4. The method for determining the reasonable height of the cast-in-place concrete according to claim 3, wherein in step S3 and step S4, the formula (3) is applied, and the basic differential equation of the elastic support first-layer beam under the foundation is as follows:
Figure FDA0002513712760000024
Figure FDA0002513712760000025
in step S4:
Figure FDA0002513712760000026
EI is the section bending rigidity;
the solution of equation (7) is:
Figure FDA0002513712760000027
the boundary condition is
Figure FDA0002513712760000028
Then: c3＝C4＝0
Order to
Figure FDA0002513712760000029
Δ' ═ cosh2 γ + cos2 γ then:
Figure FDA00025137127600000210
therefore, the temperature of the molten metal is controlled,
Figure FDA00025137127600000211
substituting the formula (8) to obtain:
Figure FDA00025137127600000212
solving to obtain:
Figure FDA00025137127600000213
5. the method for determining the reasonable height of the cast-in-place concrete according to claim 4, wherein in step S3, the basic differential equation without considering the elastic support first-layer beam under the foundation is as follows:
Figure FDA0002513712760000031
in step S4Setting:
Figure FDA0002513712760000032
EI is the section bending rigidity;
the solution of equation (8) is:
Figure FDA0002513712760000033
the boundary condition is
Figure FDA0002513712760000034
Then: c3＝C4＝0
Order to
Figure FDA0002513712760000035
Δ cosh2 α + cos2 α then:
similarly, the stress function of the elastic support first-layer beam under the foundation is not considered in the solution
Figure FDA0002513712760000036
6. The method for determining the reasonable height of the cast-in-place concrete according to claim 4, wherein in step S5, the tensile strength f of the first-layer concrete beamt，nTo compressive strength fcu，n0.05 times, i.e. ft，n＝0.05fcu，n；
In step S6, the first concrete layer does not crack, and sigma < f must be satisfiedt，nI.e. by
Considering the foundation as follows:
Figure FDA0002513712760000037
simplified backstage type (15)
Figure FDA0002513712760000038
The allowable weight of the second layer of concrete is as follows:
Figure FDA0002513712760000039
in step S7, f is allowedt，n、p0Then, the unknown quantity β of implicit function is solved by the formula (15)
Figure FDA00025137127600000310
The height allowed for the stent system is then:
Figure FDA00025137127600000311
formula (17) wherein: h (m) is the allowable height of the support system.
7. The method for determining the reasonable height of the cast-in-place concrete according to claim 5, wherein in step S5, the tensile strength f of the first-layer concrete beamt，nTo compressive strength fcu，n0.05 times, i.e. ft，n＝0.05fcu，n；
In step S6, the first concrete layer does not crack, and sigma < f must be satisfiedt，nI.e. by
Regardless of the foundation:
Figure FDA0002513712760000041
simplified backstage formula (19)
Figure FDA0002513712760000042
The allowable weight of the second layer of concrete is as follows:
Figure FDA0002513712760000043
in step S7, f is allowedt，n、p0In this way, the implicit function unknowns are solved from equation (18)
Figure FDA0002513712760000044
Then
Figure FDA0002513712760000045
Figure FDA0002513712760000046
The height allowed for the stent system is then:
Figure FDA0002513712760000047
formula (21) wherein: h (m) is the allowable height of the support system.
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